aspg-21-3238-1791475505 20261008160505 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group International Journal of Neutrosophic Science IJNS 2692-6148 2690-6805 2025 25 3 Mohammed Qassim College of the Basic Education, Mathematics Department, University of Babylon, Iraq Ahmed Hadi Hussain College of the Engineering\ Al-Musayab, Energy Engineering Department, University of Babylon, Iraq Mohammed Abed Daim Zoba College of the Engineering\ Al-Musayab, Energy Engineering Department, University of Babylon, Iraq Abdullah hamad salman College of the Basic Education, Mathematics Department, University of Babylon, Iraq Mohammed A. lafta Ministry of Education / First Rusafa Education Directorate, Iraq We employ the Laplace Residual Power Series Method to approximate analytical solutions for differential equations and neutrosophic differential equations with associated parameters, including non-homogeneous equations and fractional formulas in partial differential equations (PDEs). This approach showcases the method's simplicity, effectiveness, and robustness in deriving analytical series solutions for PDEs that involve associated parameters, especially in the context of fractional differential equations. Several practical uses of LRPSM with an emphasis on non-homogeneous and partial differential equations and neutrosophic equations with fractions (PDEs). These applications are significant in a variety of scientific and engineering domains that simulate complicated dynamic system such as anomalous diffusion in physics, viscoelastic material modeling in engineering and signal processing. 2025 14 24 3238 https://creativecommons.org/licenses/by/4.0/ 10.54216/IJNS.250302 https://www.americaspg.com/journal/21/article/3238 https://www.americaspg.com/storage/31729519500.pdf